The trouble is that when the poor fellow came to multiply by the “naught” he forgot in the first instance that it was nothing, and that the biggest number in the world multiplied by nothing will produce nothing. He knew that something ought to go down there, and so in sheer desperation he wrote down the number he was multiplying.
In the second instance, while he recognized that nothing is nothing, he forgot that all our figuring is done by columns, as we saw in our last lesson; so that when we are multiplying by tens we must put our first figure down in the hundreds column, and so on. By forgetting this he multiplied his number by two hundreds, but put his first figure down in the tens columns, and thus he really multiplied by only 28 instead of 208.
Now, the very simplest way to avoid this sort of mistake is to “go through the motions” of multiplying by the “naught” or “zero.” Thus:
| The Right Way. | 3,125 |
| 208 | |
| ——— | |
| 25000 | |
| 0000 | |
| 6250 | |
| ——— | |
| 650,000 |
This looks a little clumsy, perhaps, but it is the logical way—to go through the process of saying naught times 5 is naught, naught times 2 is naught, etc., putting down the results in the proper columns. It is the safest way, if you are the least bit weak on the principles of numbers, to do even the process of multiplying by whole hundreds. Thus:
| 3,125 |
| 200 |
| ——— |
| 0000 |
| 0000 |
| 6250 |
| ——— |
| 625,000 |
By writing his example in the “short cut” style I have seen many a man make this mistake:
| Wrong. | 3,125 |
| 200 | |
| ——— | |
| 62500 |
That is, after setting down his two surplus ciphers, when he obtained another in multiplying 5 by 2, he forgot that it was a new one and went right on to the next process. If you are in that position that you must really learn your arithmetic all over again, stick to the logical method of showing every process and learn the “short cuts” afterward.